Rewrite as a simplified fraction. ${2.7\overline{76} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2776.7676...\\ 10x &= 27.7676...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2749}$ ${x = \dfrac{2749}{990}} \text{or} {2 \dfrac{769}{990}}$